Russia denies that and counters that Europe and the United States are propping up an illegitimate government in Kiev.
"So far at least we have seen them not abide by the spirit or the letter of the agreement in Geneva," Obama said of Russia on a visit to Japan.
"We have prepared for the possibility of applying additional sanctions," he told a news conference. "There's always the possibility that Russia, tomorrow, or the next day, reverses its course and takes a different approach."
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Russian news agencies quoted Foreign Minister Sergei Lavrov as saying that he expected "the Geneva accords will be implemented in practical actions in the near future".
In NATO member Poland, the first group of a contingent of around 600 U.S. soldiers arrived on Wednesday. They are part of an effort by Washington to reassure eastern European allies who are worried by a build-up of Russian forces near Ukraine's borders.
In Ukraine, the Western-backed government said the city hall in Mariupol, which had been seized by pro-Russian separatists, was now back under central control. Interior Minister Arsen Avakov said the mayor was back in his office, and that explosives experts were checking the building to make it safe.
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"In this instance there were no casualties. And that is good and proper. The process of getting the situation back to normal in the city will continue," Avakov said in a post on his Facebook page.
Mariupol, an industrial city on the Azov Sea, was the scene of violent clashes last week when, according to the Kiev government, separatist attackers tried to storm a base of the Ukrainian national guard.
If the Mariupol city hall is indeed back under Kiev's control, it would be the first substantial sign that the Geneva accord is being implemented.
But Kiev also reported a shootout overnight in another part of the east when a Ukrainian soldier was wounded, while pro-Russian separatists who control the city of Slaviansk were holding three journalists, including U.S. citizen Simon Ostrovsky.
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Ukraine, a former Soviet republic, slipped into unrest late last year when Moscow-backed President Viktor Yanukovich rejected a pact to build closer ties with Europe. Protesters took over the centre of Kiev, eventually forcing him to flee in February.
Days later, Russian troops seized control of Ukraine's Crimea Peninsula. Moscow then annexed the region, saying it was protecting Russian residents, while the West called the action an illegal land grab.
The focus has now shifted to eastern Ukraine, the industrial heartland and home to a large Russian-speaking community.
No way back?
With rhetoric building from the United States about the imposition of a new, tougher round of sanctions, Russia suggested on Thursday that Western firms which pulled out of the country may not be able to get back in.
"It is obvious that they won't return in the near future if they sever investment agreements with us, I mean there are consequences as well," Natural Resources Minister Sergei Donskoi told reporters.
"Russia is one of the most promising countries in terms of hydrocarbons production. If some contracts are severed here, then, colleagues, you lose a serious lump of your future pie," the minister added.
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Supplies of Russian gas to Europe are also, potentially, at risk from the crisis over Ukraine. Russia has threatened to cut Kiev off unless it pays off its debts. This would have a knock-on effect on European customers further West, because many of the pipelines that deliver their gas run through Ukraine.
European and Ukrainian officials were to meet in Slovakia, which borders Ukraine, on Thursday to try to work out ways to mitigate the impact if Ukraine is cut off.
The options include reversing the usual east-west flow of the pipelines to Europe to pump gas back into Ukraine, but the volumes that could be supplied this way would be only a small fraction of the amount that Ukraine needs.
Unarmed mediators from the Organisation for Security and Cooperation in Europe are in eastern Ukraine trying to persuade pro-Russian gunmen to go home, in line with the Geneva accord.
Though there was the possibility of progress in Mariupol, there were also fresh indications of the violence that has flared several times since the accord was signed, and threatened to torpedo it.
Interior minister Avakov said troops loyal to Kiev had repelled an overnight attack on their base in eastern Ukraine. In his Facebook post, he said the raid was led by a thickly-bearded man he alleged was a Russian soldier who had been spotted previously helping the separatists.
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Reuters reporters have not been able to establish that any Russian troops or special forces members are in the region, though Kiev and Western powers say they have growing evidence that Moscow has a covert presence.
Russian President Vladimir Putin has described as "nonsense" allegations that Moscow has its forces in eastern Ukraine. It says the unrest is a spontaneous protest by local people who fear persecution from the government in Kiev which is illegitimate and has far-right links.
A Reuters reporter near Slaviansk, a flashpoint city where there is a concentration of heavily-armed pro-Russian separatists, said Ukrainian troops were fortifying a position nearby.
Kiev has said it will press ahead with an operation to crack down on the separatists - though it was not clear if its under-resourced security forces had the capacity to do that, or if it was possible without violating the Geneva accord.